The Three-Boson System at Next-To-Next-To-Leading Order

Abstract

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R^3/a_2^3). Since corrections of O(R/a_2) and O(R^2/a_2^2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.

20 pages, 3 eps figures

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• Efimov States in Nuclear and Particle Physics
• Renormalization of Singular Potentials and Power Counting
• Universal properties and structure of halo nuclei
• Low-Energy Universality in Atomic and Nuclear Physics
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons
• Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature
• Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
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• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• The ^4He trimer as an Efimov system
• Low-energy p-d scattering and He-3 in pionless EFT
• Two and Three Nucleons in a Trap and the Continuum Limit
• Benchmark helium dimer and trimer calculations with a public few-body code
• The proton-deuteron system in pionless EFT revisited
• Pion-mass dependence of three-nucleon observables
• Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length
• New Calculations of Recombination Rates for Cold ${}^4$He Atoms and Determination of Universal Scaling Functions
• Resonant three-body physics in two spatial dimensions
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Triton Photodisintegration with Effective Field Theory
• A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
• Universality Constraints on Three-Body Recombination for Cold Atoms: from 4He to 133Cs
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• An alternative scheme for effective range corrections in pionless EFT
• Effective interactions and operators in no-core shell model
• Three-body systems in physics of cold atoms and halo nuclei
• Three-body systems in pionless effective field theory
• The van der Waals interaction as the starting point for an effective field theory
• Spurious poles in a finite volume
• Scaling functions applied to three-body recombination of Cesium-133 atoms
• Universality and Leading Corrections in Few-Body Systems
• Universality in Few-Body Systems
• Effective field theory analysis of boson-trimer bond lengths to next-to-leading order
• Few-Body Effects in Cold Atoms and Limit Cycles